Just before the arrival of the Aliens (Prawns) in 1982, the UN had just started two ongoing operations:
- 1974 Ongoing UN Disengagement Observer Force
- Maintain ceasefire between Syria and Israel on the Golan Heights
- 1978 Ongoing UN Interim Force in Lebanon
- Supervise Israeli withdrawal from Lebanon. Keep the international peace and security, and help the Lebanese Government restore its effective authority in the area.
These peacekeeping missions would have stretched their forces relatively thin, so when the aliens arrived there would have been very little they could do in terms of manpower. And anyway the UN moves NATO forces in when there is conflict, not something 'suspicious'.
With no chance to force their way in three months of communication between SA and the UN is probably why no attempt was made to contact the ships (who were silent up until then) by either side. When they found the aliens were of no threat (and in fact starving and helpless) the SA government would have communicated this to the UN, I suspect the UN may have sent in some 'people' to investigate, but the UN is not a scientific group and no conflict needs settling. They would likely have told the US to back off and let the SA government handle it.
Pretty much nothing happens in the intervening decades. Nothing. No wars with the aliens, nothing of interest. It's a lot of time for everyone to settle down. Say "Yeah aliens arrived, but so what? They've been here for decades." Public interest would have died off after the initial buzz, more or less.
This is why the US and others wouldn't have gotten directly involved: No direct conflict to step in on, no 'threat' or interest. I'm sure some US scientists are working at MNU, I'm sure there is some low level involvement by the US and UN, but right now it's not interesting.